Milk costs 25 cents per liter, and cream costs 85 cents per liter. How many liters of milk must be added to 25 liters of cream to create a mixture that costs 45 per liter?

Let's denote the amount of milk needed as M (in liters).

The total cost of the mixture is the sum of the cost of the milk and the cost of the cream.

The cost of the milk is 25 cents per liter times the amount of milk (M), and the cost of the cream is 85 cents per liter times 25 liters.

The total volume of the mixture is the sum of the volumes of the milk and the cream, which is M + 25 liters.

The cost per liter of the mixture is the total cost divided by the total volume, which is 45 cents per liter.

So, we can set up the following equation:

(25M + 85*25) / (M + 25) = 45

Solving this equation for M gives us the amount of milk needed.

First, multiply both sides by (M + 25) to get rid of the denominator:

25M + 85*25 = 45(M + 25)

Then, distribute the 45 on the right side:

25M + 8525 = 45M + 4525

Subtract 45M from both sides:

-20M + 8525 = 4525

Subtract 45*25 from both sides:

-20M = -40*25

Finally, divide both sides by -20 to solve for M:

M = 50 liters

So, you need to add 50 liters of milk to the 25 liters of cream to create a mixture that costs 45 cents per liter.